1. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Modeling via Differential Equations. Analytic Technique: Separation of Variables. Qualitative Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear Differential Equations. Changing Variables. Labs for Chapter 1.

2. FIRST-ORDER SYSTEMS.

Modeling Via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. Qualitative Analysis. The Lorenz Equations. Labs for Chapter 2.

3. LINEAR SYSTEMS.

Properties of Linear Systems and the Linearity Principle. Straight-Line Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex Eigenvalues. The Special Cases: Repeated and Zero Eigenvalues. Second-Order Linear Equations. The Trace-Determinant Plane. Linear Systems in Three Dimensions. Labs for Chapter 3.

4. FORCING AND RESONANCE.

Forced Harmonic Oscillators. Sinusoidal Forcing and Resonance. Undamped Forcing and Resonance. Quantitative Analysis of the Forced Harmonic Analysis. The Tacoma Narrows Bridge. Labs for Chapter 4.

5. NONLINEAR SYSTEMS.

Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Labs for Chapter 5.

6. LAPLACE TRANSFORMS.

Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Labs for Chapter 6.

7. NUMERICAL METHODS.

Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. Labs for Chapter 7.

8. DISCRETE DYNAMICAL SYSTEMS.

The Discrete Logistic Equation. Fixed and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. Labs for Chapter 8.

HINTS AND ANSWERS.
INDEX.